Abstract
Due to the rapid development and wide application of compressed sensing and sparse reconstruction theory, there exists a series of sparsity-based methods for the antenna sensor array direction of arrival (DOA) estimation with excellent performance. However, it is known that this kind of algorithms always suffers from the problem of grid mismatch. To overcome this shortcoming, a gridless DOA estimation algorithm with finite rate of innovation (FRI) based on a symmetric Toeplitz covariance matrix is proposed for uniform linear array (ULA) in this paper. In particular, a multiple measurement vector (MMV) FRI reconstruction model is built by exploiting the covariance data denoised according to covariance fitting criteria rather than the direct data or the original covariance data, which is commonly used in other representative gridless DOA estimation methods. Next, DOA can be retrieved from the recovered covariance matrix by utilizing an annihilating filter because each covariance data is a linear combination of complex exponentials. It guarantees to produce an exact spatial sparse estimate without discretization required by existing sparsity-based DOA estimation methods. Finally, the effectiveness and superiority of the proposed algorithm are demonstrated by numerical simulations.
Highlights
As a typical problem in array signal processing, direction of arrival (DOA) estimation has found wide applications, such as radar, sonar, and wireless communications [1, 2]
By assuming that the real directions of incident sources coincide with the certain locations in presupposed discrete grids in space, on-grid sparsity-based DOA estimation algorithms represented by 1-svd method [8] transform DOA estimation into a linear sparse signal reconstruction problem
Since the grid size is greatly larger than the source number, spatial signals can be extended to a sparse vector, which is composed of virtual numerical values from candidate directions on the grid
Summary
As a typical problem in array signal processing, direction of arrival (DOA) estimation has found wide applications, such as radar, sonar, and wireless communications [1, 2]. Chen et al EURASIP Journal on Advances in Signal Processing (2020) 2020:44. Because of these attractive properties, sparsity-based DOA estimation algorithms have received extensive attention and research in the past decade. According to the relationship between real locations of sources and spatial discrete grids, the existing sparsity-based DOA estimation algorithms can be classified into three categories: on-grid, off-grid, and gridless. By assuming that the real directions of incident sources coincide with the certain locations in presupposed discrete grids in space, on-grid sparsity-based DOA estimation algorithms represented by 1-svd method [8] transform DOA estimation into a linear sparse signal reconstruction problem. DOAs of sources, which represent the locations of non-zero elements in the reconstructed signal, can be obtained by spectral peak searching
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